If you’re buying an actual photo booth, they include their own lighting.
If you’re trying to set up a ‘photo booth’ look using a pop up bg etc, you could use a couple of Godox AD200’s with pop up softboxes or shoot thru brollies.
For table shots, grab n grins etc; it’s horses for courses, some people are content with an on camera flash, bounced with a stofen or similar. I preferred a bit more flexibility, with hand held flash bouncing or direct, often with OCF to create a starburst for first dance, or to use as a backlight. Others set up a couple of off camera lights on stands to bounce off the ceiling as floods, there’s dozens of ‘right’ ways to do it.
The short answer is to think about a selection of off camera lighting, I’d recommend Godox for scalability (3 or 4). A couple of stands, a trigger, and a couple of brackets, softboxes, or brolly boxes. You can start w 2 speedlights, but adding AD200’s, then something like an AD600 to stretch your capability into lighting in bright sun would be ideal to cover all eventualities.